L23-stats-post

xn iid exponential n max e x i i1 xi i1 ml

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Unformatted text preview: error Θ Maximum Likelihood Estimation • Model, with unknown parameter(s): X ∼ pX (x; θ) • Pick θ that “makes data most likely” ˆ θML = arg max pX (x; θ) θ • Compare to Bayesian MAP estimation: pX |Θ(x|θ)pΘ(θ) ˆ θMAP = max θ pX (x) • Example: X1, . . . , Xn: i.i.d., exponential(θ) n max θ θ e− θ x i i=1 θ xi i=1 ˆ θML = n/(x1 + . . . + xn) ˆ Θn = ˆ • Unbiased: E[Θn] = θ – exponential example, with n = 1: E[1/X1] = ∞ = θ (biased) ˆ • Consistent: Θn → θ (in probability) – exponential example: (X1 + · · · + Xn)/n...
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This note was uploaded on 06/04/2013 for the course EE 6.431 taught by Professor Johntsitsiklis during the Spring '10 term at MIT.

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